2023-03-22T16:14:16Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/455232022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Large time behavior of the vorticity of two‐dimensional flow and its application to vortex formationGiga, Y.Kanbe, T.open access35-xx PARTIAL DIFFERENTIAL EQUATIONS410We consider the Cauchy problem for the two-dimensional vorticity equation. We show that the solution ω behaves like a constant multiple of the Gauss kernel having the same total vorticity as time tends to infinity. No particular structure of initial data ω = ω(x,0) is assumed except the restriction that 0 the Reynolds number R = ſlω0 ldx/v is small, where v is the kinematic viscosity. Applying a time-dependent scale transformation, we show a stability of Burgers' vortex, which physically implies formation of a concentrated vortex.Department of Mathematics, Hokkaido University1987-05engdepartmental bulletin paperVoRhttps://doi.org/10.14943/48746http://eprints3.math.sci.hokudai.ac.jp/358/http://hdl.handle.net/2115/4552310.14943/48746Hokkaido University Preprint Series in Mathematics2244https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/45523/5/pre2.pdfapplication/pdf1.06 MB1987-05